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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>Thus,</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
Y=1\cdot \int \frac{x (-2) }{2} \textrm{d} x+e^x \int \frac{x e^{-x}}{2} \textrm{d} x+e^{-x} \int \frac{x e^x}{2} \textrm{d} x=-\frac{1}{2} x^2-1.
\end{equation*}
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<p class="continuation">The general solution is</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
y=C_1+C_2 e^x+C_3 e^{-x}-\frac{x^2}{2}-1=C_1+C_2 e^x+C_3 e^{-x}-\frac{x^2}{2},
\end{equation*}
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<p class="continuation">where <span class="process-math">\(C_1, C_2, C_3\)</span> are updated arbitrary constants.</p>
<span class="incontext"><a href="sec4_4.html#p-173" class="internal">in-context</a></span>
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